Question

what is the velocity of a carbon dioxide molecule at 25 degrees centigrade in a one cubic foot box

Answer 1

Answer on Question #53783, Physics Quantum Mechanics

what is the velocity of a carbon dioxide molecule at 25 degrees centigrade in a one cubic foot box

Solution

The RMS velocity of a carbon dioxide molecule is given by Eq.(1)

$$\sqrt {\left\langle v ^ {2} \right\rangle} = \sqrt {\frac {3 R T}{\mu}} = \sqrt {\frac {3 \cdot 8 . 3 1 J / K \cdot m o l \cdot 2 9 8 K}{4 4 \cdot 1 0 ^ {- 3} k g / m o l}} = 4 1 1 m / s$$

where $M = 44 \cdot 10^{-3} \, \text{kg/mol}$ is the molar mass; $R = 8.31J / K \cdot \text{mol}$ is the gas constant; $T = 273 + 25 = 298K$ is the absolute temperature.

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